Questions tagged [beam]

Questions about the theory and applications of structural elements designed to resist bending.

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Any way to approximate effect of two point loads with just one?

Imagine a 3D problem where the goal is to calculate the max. cantilever beam deflection. There are 4 equal point loads A, B,C,D separated equally from the beam's major axis. Is there a way to ...
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Max bending moment estimate

Context: I study aerodynamics and want to design and build an RC wing to put the theory I learned into practice. The essence of the theory I learned is: Given some mass of wing building material, how ...
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Magnitude of shear stress on beam element

In a previous question, the existence of a horizontal shear stress in a cantilevered I-beam with one free end was resolved. Here I'd like to explore the magnitude of the shear stress. Consider an I-...
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Direction of shear in beam cross section - how to understand the convention

In an I-beam, the shear flow is usually shown drawn as on the left, not as drawn on the right. I do not understand why. I do understand: The total horizontal shear force must be zero, consistent with ...
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How can I understand shear flow in a beam cross section?

I am trying to understand shear flow and I am just not getting it. For example, one of the problems in Beer has an I-beam and there is both a horizontal and vertical force acting on it. So it has ...
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Are there disadvantages to using a single multispan beam, vs separate simple beams, for materials that tolerate tension as well as compression?

Suppose the following beam situation within a mundane building (viewed from above). Assume vibration and torsion aren't issues. Suppose we have a choice to span a gap in 2 different ways: (Grey = ...
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Does the corbel angle govern in this scenario? If not, how is load spreading allowed for, when a load is supported by a wall on a beam

The following outline is inspired by something I noticed today and couldn't figure out. It shows what I guess is a fairly common generic situation - an upper floor masonry partition wall supported by ...
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Analysing a multispan determinate beam by separating it into spans

Say we have the following indeterminate beam: We can make it determinate by adding a pin at B, and then adding back the bending moment at B which was destroyed by the pin: My lecture handouts then ...
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Composite Cantilever Beam Analysis

I'm trying to solve this composite cantilever beam for deflection analysis. How should I proceed? I'm not from mechanical background. The connection between the elements is strong enough that the ...
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Simply supported beam with a truss

i am trying to find out the best way to approach a design task for a plane wing with a truss support. i am treating the wing as a simply supported beam but i have no idea how to incorporate the truss ...
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Rigidity and bending moment

When a beam which is fixed at one end and free at the other, is acted upon by a load P, the beam bends and we get a bending moment at every cross section of the beam. This bending moment can be ...
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What's the best shape (solid of revolution) for a cantilever beam to carry a point load at the free end?

How should you change the diameter/radius (while keeping constant overall volume) of the cross-section along the length of a round cantilever beam so that you minimise deflection with concentrated ...
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Maximum deflection in the beam

Consider a simply supported beam, acted upon by a concentrated load P as shown By applying the method of successive integration, i.e. by using the differential equation $$EI \frac{d^2v}{dx^2} = M$$ ...
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Forces supporting a beam

I've been struggling with this engineering problem. The forces I've got are Frb=2.08kN, Fray=15.12kN, and Frax=3kN. Before i give in my calculations I need to do a check if they are correct or not ...
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Why the vertical shear stress in the flange neglected?

Consider a thin walled I section beam. At some intermediate c/s the shear force is V. The shear stress direction in flanges and web will be as shown. The textbook says that, the vertical shear ...
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How exactly the beam is twisting?

Consider an I section beam shown below, which is unsymmetric about the x-y plane. I apply a load P, at the centroid of this section. The textbook I follow, says that the member will twist apart from ...
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First moment of area about the neutral axis

Consider a homogeneous beam with a rectangular c/s, its neutral axis will be at equal distances from the top and bottom edges. The first moment of the entire area about the NA will be zero, since we ...
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Should the stiffness of this cantilever beam be different for these two conditions?

So, I was just doing some Finite Element Analysis (FEA) to figure out what would be the effect on the stiffness of a cantilever beam if another beam is attached to it on its free end. Below shows the ...
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How are beams arranged in a continuous concrete beam structure?

I am posed with this problem, where I am tasked to design multiple structural beams supporting a concrete slab. As a disclaimer, this problem is merely an exercise instead of a homework or a test, and ...
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Why in a rectangular cross section beam the shear stresses are parallel to the height throughout the surface?

Consider a beam with a rectangular c/s subjected to some arbitrary loading. At any cross section the shear force is V. This shear force is the resultant of all the internal resistive forces which act ...
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Are there any stresses on this plane in a beam?

Consider a cantilever beam with a point load at its free end. If we cut the beam through a plane as shown (in which the load lies), to divide the beam into two parts, and if we isolate individual ...
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Direction of Shear Stress on the periphery of a circular section beam

The Question is from shear stresses in beams Consider a beam made of circular cross section, in which at any cross section the shear force is V. The textbook I'm following states that - When a beam ...
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How is the limit state EQU used in Eurocode?

Quote from here: Limit state EQU, dealing with static equilibrium, is defined as: Loss of static equilibrium of the structure... considered as a rigid body, where minor variations in the [actions or ...
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Due to what reason are the beams getting elongated?

I was studying about shear stresses in beams, where one of the ways the textbook tried explaining intuitively the presence of shear stresses in beams was: Source : Mechanics of Materials, R.C. ...
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Proving the advantage of a composite beam

The textbook that I'm following for studying bending stresses in beams, states that - "Engineers purposely design beams in this manner (composite manner) in order to develop a more efficient ...
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Determining the ratio of bending moments in parts of a composite beam

Consider a composite beam formed by sandwiching a wood beam between two steel plates, whose cross section is shown. Say the beam is loaded by some arbitrary loading, due to which at any cross section ...
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Beam of uniform strength

Generally, for a given loading condition, the bending moment in a beam varies throughout its length due to which the maximum normal/bending stress at every section is different. For a given allowable ...
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Dimensions of the wooden post

This question is regarding the following problem from Bending stresses in beams Problem: My solution and hence the answer doesn't match with the answer in the textbook. My Solution: The planks A will ...
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How is the wire in this problem in pure bending?

Problem: A beam is said to be in pure bending if the bending moment in it remains constant throughout the length. The problem asks to determine the bending moment in the wire. In the solution of the ...
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Confusion about sign of beam's moment force

A positive bending moment bends a beam concave upward(or towards the positive y direction), whereas a negative bending moment bends a beam concave downward(or towards the negative y direction). (...
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Moment equilibrium equation of beam

The above beam is loaded by a distributed load per unit length of the referential scale defined by the vector field q = q(x) and a distributed moment load vector per unit length m = m(x). As a ...
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Derivation of beam deflection equation

I have encountered the above beam deflection equation for a beam subjected to a linearly increasing distributed load while I was solving bisection method (https://itprospt.com/qa/159961/q3-15-points-...
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How does one conclude from this, that neutral axis passes through the centroid?

The book I'm following for Strength of materials states that, in a beam with symmetric cross section (about the plane of bending) and in pure bending, the moment of cross sectional area about the ...
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Deflection of Cantilever Beam with Midpoint Spring, Integration and Superposition Methods

How can I get the deflection required below using 1) the Integration and 2) Superposition methods (two ways)? The beam $AB$ is supported by a spring $CD$, which is fixed at $C$ with constant $k$, and ...
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A problem on beams

Problem - I have interpreted "by hinging them together at B" as following - Now if this is the case, then applying a load on the right beam will have no effect, in my understanding, on ...
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Slope of the Bending moment diagram where a point force acts

Consider a beam that is arbitrarily loaded and at any distance x, we take an element in the beam between two sections, where a point force acts as shown. Let us assume the directions of shear force ...
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Solving Timoshenko beam equation for cantilever beam

Update with solution Solution 1 Problem: Beam clamped at left side, free end on right side, point load pointing downwards. x is defined positive from the clamped end towards the free end. Create FBD ...
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How is load bearing capacity of a leg of steel angle calculated?

Suppose a section of steel angle is used to support a structural beam, which would otherwise have no available bearing, as in the following sketch. Assuming that appropriate connection/fixing on the ...
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How is the thickness of a steel plate underslung beneath a beam, to be calculated? (UK/EU)

A common way of providing bearing for concrete floor-beams above ground level, is to create a "slimflor" style steel element, comprising an "I" beam with a steel plate welded ...
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Can we use the Flexural formula and the Beam theories for bodies made up of Composite materials?

Below shows a link for the derivation of Flexural formula. Derivation of Flexural formula In this above link, there are a few assumptions made to reach to its final form. They are shown below. By ...
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What is a shear release? [closed]

For my statics project, we are being asked to draw the shear and bending moment diagram for a beam, which is usually pretty straightforward. However, here there is something called a shear release on ...
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Can the general Flexural formula be used in the case of transverse loading of a beam?

The general derivation of the Flexural formula uses the pure bending case, where the distance from a curved section to the neutral axis is assumed to be constant even after bending, denoted by y. The ...
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Design procedure used in beam design

In the design of beams, the principal stresses and absolute maximum shear stresses are not calculated. Instead, we calculate maximum bending stress using flexure formula and equate it to allowable ...
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Modeling the Internal Forces Exerted on a Catapult Arm while Throwing

I am currently creating a MATLAB script to determine the internal forces present in a uniform beam as it is accelerated by a torsional spring. I was able to derive the equation for the axial force ...
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Why can't I-beam resist torsion but can resist shear stress due to transverse loading?

It is already known that the I-beam is very bending resistant (causes less deflection for the same transverse load and also results in lesser stresses relatively). But for an eccentric transverse load ...
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Beam with width tending to zero

Suppose a cantilever beam (of rectangular cross-section) subjected to vertical transverse shear load at free end. If I consider any arbitrary cross-section then both bending and shear stress will be ...
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Why shouldn't we use Bernoulli beam theory if deformations and rotations are large?

I was going through the basic assumptions made by Bernoulli beam theory. I realized that one of the most important assumption in this theory is that the deformations and rotations of the beams are ...
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Is bending moment along a beam independent of the cross sectional area of the beam?

We know this that if the a cantilever beam (of any cross section) is fixed at one end and a transverse force is applied on the other, then it will bend. However, we just casually assume that the ...
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Why am I seeing a moment reaction at the supports for these beams in FEM?

Please observe the Finite Element model below, in ANSYS WorkBench, (Remote force behavior = Deformable). Also, please take a lot at the force and moment reactions at the fixed supports. I couldn't ...
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When we replace supports distributed reaction by point reaction in thin beams, is that considered an application of Saint-Venant principle?

I read about Saint-Venant principle which is about the effect of replacing forces by equivalent forces system that effect on the same small region of a rigid body, all examples I come across are on ...
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